Block #2,594,663

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/1/2018, 12:23:53 AM · Difficulty 11.2988 · 4,236,982 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
cdf3edbe8317c755f4b9cf60889f8a6dec41be7ac7bb9ba043cbc961161fd284

Height

#2,594,663

Difficulty

11.298764

Transactions

3

Size

1.36 KB

Version

2

Bits

0b4c7bd0

Nonce

4,944,431

Timestamp

4/1/2018, 12:23:53 AM

Confirmations

4,236,982

Merkle Root

6af58b830f2c8bf39064a28bccf922615de4e82e80f34913f4352fa04ac364de
Transactions (3)
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.331 × 10⁹⁷(98-digit number)
53318857350971621797…23314655826736988161
Discovered Prime Numbers
p_k = 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
5.331 × 10⁹⁷(98-digit number)
53318857350971621797…23314655826736988161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.066 × 10⁹⁸(99-digit number)
10663771470194324359…46629311653473976321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.132 × 10⁹⁸(99-digit number)
21327542940388648719…93258623306947952641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.265 × 10⁹⁸(99-digit number)
42655085880777297438…86517246613895905281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.531 × 10⁹⁸(99-digit number)
85310171761554594876…73034493227791810561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.706 × 10⁹⁹(100-digit number)
17062034352310918975…46068986455583621121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.412 × 10⁹⁹(100-digit number)
34124068704621837950…92137972911167242241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.824 × 10⁹⁹(100-digit number)
68248137409243675901…84275945822334484481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.364 × 10¹⁰⁰(101-digit number)
13649627481848735180…68551891644668968961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.729 × 10¹⁰⁰(101-digit number)
27299254963697470360…37103783289337937921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.459 × 10¹⁰⁰(101-digit number)
54598509927394940720…74207566578675875841
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,897,265 XPM·at block #6,831,644 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy Policy·

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy